Preheat your oven to 400°F (200°C).
In a small saucepan over medium heat, melt the butter. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.
Stir in the lemon zest, lemon juice, dried parsley, salt, and black pepper. Remove from heat and set aside.
In a large oven-safe skillet, heat the olive oil over medium-high heat. Add the cod fillets and sear for about 2-3 minutes on each side until golden brown.
Pour the garlic butter mixture over the cod fillets, ensuring they are well coated.
Transfer the skillet to the preheated oven and bake for 10-12 minutes, or until the cod flakes easily with a fork.
Remove from the oven and let it rest for a couple of minutes before serving with lemon wedges.